Faster WIND: Accelerating Iterative Best-of-$N$ Distillation for LLM Alignment

Recent advances in aligning large language models with human preferences have corroborated the growing importance of best-of-$N$ distillation (BOND). However, the iterative BOND algorithm is prohibitively expensive in practice due to the sample and computation inefficiency. This paper addresses the problem by revealing a unified game-theoretic connection between iterative BOND and self-play alignment, which unifies seemingly disparate algorithmic paradigms. Based on the connection, we establish a novel framework, \textbf{WIN} rate \textbf{D}ominance~(WIND), with a series of efficient algorithms for regularized win rate dominance optimization that approximates iterative BOND in the parameter space. We provides provable sample efficiency guarantee for one of the WIND variant with the square loss objective. The experimental results confirm that our algorithm not only accelerates the computation, but also achieves superior sample efficiency compared to existing methods.